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Weighted projective spaces are natural generalizations of projective spaceswith a rich structure. Projective Reed-Muller codes are error-correcting codesthat played an important role in reliably transmitting information on digitalcommunication channels. In this case study, we explore the power of commutativeand homological algebraic techniques to study weighted projective Reed-Muller(WPRM) codes on weighted projective spaces of the form $\mathbb{P}(1,1,a)$. Wecompute minimal free resolutions and thereby obtain Hilbert series for thevanishing ideal of the $\mathbb{F}_q$-rational points, and compute mainparameters for these codes.

Algebraic Invariants of Codes on Weighted Projective Planes